Page 70 - Introduction to chemical reaction engineering and kinetics

52 Chapter 3: Experimental Methods in Kinetics: Measurement of Rate of Reaction

first be assumed to calculate values of the ordinate. (A nonlinear method of determining
values of the parameters from experimental data may be used instead, but we focus on
linear methods that can be demonstrated graphically in this section.)

As noted in equation 3.4-9, the form given there is not applicable to a first-order rate law
(why not?). For n = 1, what is the form corresponding to equation 3.4-9?

SOLUTION

If n = 1, equation 3.4-9 becomes indeterminate (kAt = O/O). In this case, we return to
equation 3.4-8, which then integrates to

cA = c,,exp(-kAt) (n = 1) (3.4-10)

or, on linearization,

ln CA = ln CA0 - kAt (n = 1) (3.4-11)

As illustrated in Figure 3.5, a linear relation for a first-order reaction is obtained from a plot
of In CA versus t. (The result given by equation 3.4-10 or -11 can also be obtained directly
from equation 3.4-9 by taking limits in an application of L’HBpital’s rule; see problem
3-8.)

If the rate law involves more than one species, as in equation 3.4-3, the same general
test procedure may be used, but the integrated result depends on the form of the rate
law.

What is the integrated form of the rate law (-rA) = kAcAcB for the reaction Iv,lA +
1 in (B + products carried out in a constant-volume BR?